The present invention relates to active filters, and more particularly, to active filters at high frequencies using low gain amplification stages.
In order to appreciate the present invention of high frequency active filters, a comparison between active and passive filters is pertinent. Passive filters were the forerunners of active filters, and much of the basic theory carried over. (Crystal and mechanical filters can be reasonably classified with passive filters.) Digital filters are the next step beyond analog active filters, although a direct comparison is not completely fair inasmuch as a digital filter usually requires an analog prefilter and post filter.
The requirement of a power supply for active filters is no longer a significant handicap although active filters do require better regulation while digital filters usually require more power. Passive filters have virtually no high-frequency limit, but become bulky below 10 KHz and are virtually unacceptable below 1 KHz. Active filters suit the mid-range from 1 Hz to 1 KHz, but can be used with some care to 10 KHz and in limited applications can be used as high as 100 KHz. Passive filters usually must be impedance-matched on both input and output while active filters normally have a high enough input impedance and a low enough output impedance that impedance is not a problem. Some types of passive filters can have many sections, e.g., 23-pole crystal filters are common. Active filter design becomes difficult beyond 10 poles. Similarly, with dynamic range, passive filters have no inherent limit beyond practical considerations such as the size of inductances on the low end and parasitic capacitance or load and other inductances at the high end. Active filters are limited by power supply on the high end and semiconductor noise on the low end. Additionally, passive filters are expensive and bulky primarily because of inductors. Passive filters often show large discrepancies between calculated and actual performance, while active filters calculations tend to be good, especially if tolerance errors are accounted for.
A filter is usually specified as an amplitude response versus frequency curve. For example, an ideal low-pass filter would have rectangular characteristics with the passband perfectly flat, the transition band being infinitely steep, and the reject band having complete rejection everywhere. However, such a filter cannot be built, at least not with a finite number of parts. A more realistic filter is to add a finite slope. However, it turns out that this is still unrealizable because the corner is infinitely sharp. If the corner is rounded, the characteristic may be achievable. Additionally, the filter is not completely specified without adding phase response which often is ignored. Therefore, filter transfer functions are usually specified by polynominals, or more precisely by a ratio of polynominals, such as: ##EQU1## Each term after the first in either the numerator or the denominator creates one bend in the amplitude response curve, which also corresponds to one reactive component in a circuit. Thus a ratio of finite polynominals implies a finite number of components.
To change a low-pass function to a high-pass function, S is replaced by 1/S everywhere in the polynominal. It can be shown that the new prototype circuit may be obtained by replacing each capacitor with an inductor (and vice-versa if necessary). This is not directly applicable herein because one of the reasons for using active filters in the first place was to avoid inductors. Further transformations may or may not be possible to eliminate the inductors. Alternately, in some circuits the resistors and capacitors may be simply interchanged. The component values are inverted because the impedance of a capacitor is inversely proportional to its value.
Likewise, a low-pass may be transformed to a bandpass by replacing S by S+1/S in the polynominal, which replaces each capacitor with a capacitor in parallel with an inductor.
Previous designs, except for the simplest functions, used op-amps. Op-amps (operational amplifiers) must have very high (virtually infinite) gain, but yet be stable with the output connected directly to the (inverting) input (negative feedback). This is a difficult requirement and thus, op-amps have stability problems and do not work well at high frequency.
Accordingly, it is desirable to provide a simple, concise, unified method for building any type of high frequency active filter without using unstable, very high gain op-amps.
Accordingly, it is an object of the present invention to provide high frequency active filters which are stable at said high frequencies without the use of high gain op-amp's.
Further objects and advantages of the present invention will become apparent as the following description proceeds and features of novelty characterizing the invention will be pointed out with particularity in the claims annexed to and forming a part of this specification.